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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 566 · 40 sums
TalentJR

The trick (Paravartya Yojayet): For ax + by = c and dx + ey = f: bottom = a×e − b×d. x = (c×e − b×f) ÷ bottom; y = (a×f − c×d) ÷ bottom. Special case ax + by = c, bx + ay = f: add the equations to get x + y, subtract to get x − y, then add and halve. Check your x and y in the first equation.

NameDateTime takenScore ___ / 40
  1. 1.6x + 2y = 40 and 3x − 3y = 0 →
  2. 2.3x + 4y = 43 and x − 2y = 1 →
  3. 3.6x + 5y = 57 and 5x + 6y = 64 →
  4. 4.x + y = 7 and x − 4y = −3 →
  5. 5.6x + 2y = 42 and 3x − 3y = 9 →
  6. 6.6x + y = 33 and x + 6y = 58 →
  7. 7.2x − 3y = −10 and 2x + y = 6 →
  8. 8.7x + 3y = 8 and 3x + 7y = −8 →
  9. 9.6x + 7y = −38 and 7x + 6y = −40 →
  10. 10.7x + 3y = 39 and 3x + 7y = −29 →
  11. 11.4x + 5y = 77 and x + 2y = 26 →
  12. 12.x − 6y = −13 and 4x + 2y = 0 →
  13. 13.4x + 3y = 25 and 2x − 4y = −26 →
  14. 14.4x − 3y = 3 and x − 5y = 39 →
  15. 15.x + 8y = 33 and 8x + y = 75 →
  16. 16.x − y = −8 and 2x + 6y = −24 →
  17. 17.3x + 2y = −19 and 2x + 5y = −9 →
  18. 18.3x + 9y = 48 and 9x + 3y = 72 →
  19. 19.5x + 3y = 37 and 4x + y = 24 →
  20. 20.2x + 5y = 45 and 5x + 2y = 39 →
  21. 21.x + 2y = 7 and 4x + 2y = −8 →
  22. 22.5x − 2y = −16 and 2x + 3y = −33 →
  23. 23.3x − y = 23 and x + 6y = 33 →
  24. 24.4x + y = −4 and 5x − 5y = 45 →
  25. 25.9x + 7y = 48 and 7x + 9y = 48 →
  26. 26.3x + 4y = 7 and 2x − y = 1 →
  27. 27.5x + 2y = −39 and 4x + 4y = −24 →
  28. 28.5x − 5y = −20 and 2x − 5y = −17 →
  29. 29.x + y = −5 and 3x + 2y = −17 →
  30. 30.3x + y = 15 and 6x − y = 57 →
  31. 31.6x − 2y = −10 and 4x − 6y = −44 →
  32. 32.x + 3y = 25 and 3x + y = 11 →
  33. 33.3x + 4y = 44 and 4x + 6y = 64 →
  34. 34.6x + 2y = 50 and 2x + 6y = 22 →
  35. 35.3x + 4y = 23 and 6x + 6y = 42 →
  36. 36.2x + 2y = 26 and 5x + 3y = 57 →
  37. 37.6x + 5y = 61 and x − 5y = −19 →
  38. 38.x − 4y = 8 and x − 5y = 9 →
  39. 39.6x + 6y = 54 and 4x + 5y = 37 →
  40. 40.7x + 4y = 63 and 4x + 7y = 69 →

Answer key

  1. x = 5, y = 5
  2. x = 9, y = 4
  3. x = 2, y = 9
  4. x = 5, y = 2
  5. x = 6, y = 3
  6. x = 4, y = 9
  7. x = 1, y = 4
  8. x = 2, y = −2
  9. x = −4, y = −2
  10. x = 9, y = −8
  11. x = 8, y = 9
  12. x = −1, y = 2
  13. x = 1, y = 7
  14. x = −6, y = −9
  15. x = 9, y = 3
  16. x = −9, y = −1
  17. x = −7, y = 1
  18. x = 7, y = 3
  19. x = 5, y = 4
  20. x = 5, y = 7
  21. x = −5, y = 6
  22. x = −6, y = −7
  23. x = 9, y = 4
  24. x = 1, y = −8
  25. x = 3, y = 3
  26. x = 1, y = 1
  27. x = −9, y = 3
  28. x = −1, y = 3
  29. x = −7, y = 2
  30. x = 8, y = −9
  31. x = 1, y = 8
  32. x = 1, y = 8
  33. x = 4, y = 8
  34. x = 8, y = 1
  35. x = 5, y = 2
  36. x = 9, y = 4
  37. x = 6, y = 5
  38. x = 4, y = −1
  39. x = 8, y = 1
  40. x = 5, y = 7

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